A triangle has corners at #(3 ,4 )#, #(4 ,7 )#, and #(2 ,8 )#. How far is the triangle's centroid from the origin?

Question

A triangle has corners at #(3  ,4  )#, #(4  ,7  )#, and #(2   ,8  )#.  How far is the triangle's centroid from the origin?

Maverick Smith · Accepted Answer

≈ 7 units

The first step here is to find the coordinates of the centroid (# x_c" and " y_c)# If # (x_1,y_1) , (x_2,y_2)" and " (x_3,y_3)# are the coordinates of the vertices of a triangle , then # x_c = 1/3(x_1 + x_2 + x_3) " and " # # y_c = 1/3(y_1 + y_2 + y_3)# here #x_c = 1/3(3+4+2) = 3" and " y_c=1/3(4+7+8)= 19/3# coordinates of centroid #= (3 , 19/3)# To calculate the distance the centroid is from the origin use the #color(blue)" distance formula " # #color(red)(|bar(ul(color(white)(a/a)color(black)( d =sqrt((x_2 - x_1)^2 + (y_2 -y_1)^2))|)))# where # (x_1,y_1)" and " (x_2,y_2)" are 2 points "# The 2 points here are the centroid and the origin Since the origin (0,0) is one of the points this simplifies the distance formula to # d =sqrt(3^2 + (19/3)^2)=sqrt(9+361/9) ≈ 7 "units"#

Aaliyah Anderson · Answer

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Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can beTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

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Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculatedTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

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Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated byTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

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Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by findingTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

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To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average ofTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

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ForTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the givenTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the xTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangleTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle withTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinatesTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 +To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3,To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 +To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4),To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2)To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4,To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) /To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7),To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 =To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), andTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
AverageTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average yTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), weTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate =To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we canTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plugTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug inTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 +To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in theseTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these valuesTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values intoTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 +To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into theTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula toTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8)To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to findTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) /To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find theTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroidTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 =To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (GTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\leftTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (roundedTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\fracTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded toTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to twoTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimalTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal placesTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3},To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

SoTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So,To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 +To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangleTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle isTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 +To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is atTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3,To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\rightTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right)To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

NowTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now,To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ GTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, toTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to findTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\leftTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distanceTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\fracTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance betweenTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid andTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3},To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the originTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin,To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \fracTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, weTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we canTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can useTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distanceTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\rightTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formulaTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right)To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \textTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance}To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ GTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(xTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\leftTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 -To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - xTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3,To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \fracTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 +To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (yTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\rightTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right)To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 -To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - yTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

NowTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now,To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, toTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find theTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distanceTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance betweenTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

WhereTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 -To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
-To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - yTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates ofTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroidTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3,To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

PlTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in theTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinatesTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
-To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates ofTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- \(To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of theTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- \( (To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroidTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- \( (x_To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- \( (x_2, yTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- \( (x_2, y_2To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3,To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- \( (x_2, y_2)To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- \( (x_2, y_2) \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3)To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) andTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates ofTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the originTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the originTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0,To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0,To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0),To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we getTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \textTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ dTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{DistanceTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d =To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance}To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} =To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrtTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 -To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 -To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 +To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 +To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \leftTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\fracTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 -To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3}To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} -To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2}To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\rightTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \textTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2}To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{DistanceTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance}To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} =To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ dTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d =To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrtTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrtTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \leftTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\fracTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2}To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\rightTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \textTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance}To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2}To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} =To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrtTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ dTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d =To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 +To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrtTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.068To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 +To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689}To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 +To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \textTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{DistanceTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}}To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} =To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ dTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrtTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d =To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrtTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.068To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\fracTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689}To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}}To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \textTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{DistanceTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance}To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ dTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approxTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d =To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 \To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

\[ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10}To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

ThereforeTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore,To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

SoTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distanceTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So,To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance betweenTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, theTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroidTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distanceTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid ofTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance betweenTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between theTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangleTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid ofTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangle andTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid of theTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangle and theTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid of the triangle andTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangle and the originTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid of the triangle and theTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangle and the origin isTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid of the triangle and the originTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangle and the origin is approximatelyTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid of the triangle and the origin isTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

$$ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Where:
- $ (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangle and the origin is approximately To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid of the triangle and the origin is $To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where:
- \( (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangle and the origin is approximately 7To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid of the triangle and the origin is $ \To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where:
- \( (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangle and the origin is approximately 7 unitsTo find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid of the triangle and the origin is $ \sqrtTo find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where:
- \( (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangle and the origin is approximately 7 units.To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid of the triangle and the origin is $ \sqrt{To find the centroid of a triangle, you take the average of the x-coordinates and the average of the y-coordinates of its vertices. Then, you can use the distance formula to find the distance between the centroid and the origin.

Given the vertices of the triangle are (3, 4), (4, 7), and (2, 8), the centroid can be calculated by finding the average of the x-coordinates and the average of the y-coordinates:

Average x-coordinate = (3 + 4 + 2) / 3 = 3
Average y-coordinate = (4 + 7 + 8) / 3 = 6.33 (rounded to two decimal places)

So, the centroid of the triangle is at (3, 6.33).

Now, to find the distance between the centroid and the origin, we can use the distance formula:

\[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Where:
- \( (x_1, y_1) $ is the coordinates of the centroid (3, 6.33).
- $ (x_2, y_2) $ is the coordinates of the origin (0, 0).

$$ \text{Distance} = \sqrt{(0 - 3)^2 + (0 - 6.33)^2} $$

$$ \text{Distance} = \sqrt{(-3)^2 + (-6.33)^2} $$

$$ \text{Distance} = \sqrt{9 + 40.0689} $$

$$ \text{Distance} = \sqrt{49.0689} $$

$$ \text{Distance} \approx 7 $$

Therefore, the distance between the centroid of the triangle and the origin is approximately 7 units.To find the centroid of a triangle with vertices at (x1, y1), (x2, y2), and (x3, y3), the coordinates of the centroid (G) can be calculated using the formula:

$$ G\left(\frac{x_1 + x_2 + x_3}{3}, \frac{y_1 + y_2 + y_3}{3}\right) $$

For the given triangle with vertices (3, 4), (4, 7), and (2, 8), we can plug in these values into the formula to find the centroid (G).

$$ G\left(\frac{3 + 4 + 2}{3}, \frac{4 + 7 + 8}{3}\right) $$

$$ G\left(\frac{9}{3}, \frac{19}{3}\right) $$

$$ G\left(3, \frac{19}{3}\right) $$

Now, to find the distance between the centroid and the origin (0, 0), we can use the distance formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of the centroid (3, 19/3) and the origin (0, 0), we get:

$$ d = \sqrt{(3 - 0)^2 + \left(\frac{19}{3} - 0\right)^2} $$

$$ d = \sqrt{3^2 + \left(\frac{19}{3}\right)^2} $$

$$ d = \sqrt{9 + \frac{361}{9}} $$

$$ d = \sqrt{\frac{9 \cdot 9 + 361}{9}} $$

$$ d = \sqrt{\frac{90}{9}} $$

$$ d = \sqrt{10} $$

So, the distance between the centroid of the triangle and the origin is $ \sqrt{10} $ units.

Sophia Alfred · Answer

undefined The centroid of a triangle can be found by averaging the coordinates of its vertices. In this case, the coordinates of the centroid are:

$$
\left(\frac{{3 + 4 + 2}}{3}, \frac{{4 + 7 + 8}}{3}\right)
$$

Solving this gives the centroid coordinates as (3, 6.33). To find the distance between this point and the origin, you can use the distance formula:

$$
\text{{Distance}} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
$$

where (x1, y1) is the origin (0, 0) and (x2, y2) is the centroid. Plugging in the values:

$$
\text{{Distance}} = \sqrt{(3 - 0)^2 + (6.33 - 0)^2}
$$

$$
\text{{Distance}} = \sqrt{3^2 + 6.33^2}
$$

$$
\text{{Distance}} \approx \sqrt{9 + 40.1289}
$$

$$
\text{{Distance}} \approx \sqrt{49.1289}
$$

$$
\text{{Distance}} \approx 7.00
$$

So, the distance from the centroid to the origin is approximately 7.00 units.